There are more clues for the second blank, so start there. The word in the second blank describes Barry's approach. You are told in the second sentence that 's shooting strategy is "unconventional." Thus a good prediction for the second blank is unconventional. Of the choices, the word closest in meaning to unconventional is unorthodox. Now look at the first blank: if Barry continued using the strategy, then how did he feel about "his contemporaries' dismissal"? A good prediction would be unconcerned with. Of the choices, the word closest in meaning to unconcerned with is nonplussed by.